It turns out that there is a very nice explanation for why your guess works. If you set r1c4=3, then the only remaining 3 in row 3 will be in r3c7. Now the only remaining 6 in box 3 will be in r1c8. Look closely now at the 4 cells r1c1, r2c1, r1c9, r2c9. Starting with the assumption r1c4=3, we get that all 4 of the above cells can only be 5 or 7. This is what is known as a deadly pattern and must be avoided at all costs. Therefore, r1c4 cannot be a 3 and hence must be a 5. As you pointed out, this solves the puzzle.

Ronk wrote:Even when used in a loop, I think it's still a Type 3 Unique Rectangle to most of us.

I don't see a bivalue cell with candidates "3,6" in row 1 in order for it to be a Type-3 Unique Rectangle. Do you Ronk? Well, in spite of the apparent fact that it looks an UR for most of "you", it is still an AUR for me. Good try Ronk, but you didn't convince me, sorry.Also, I think what is really important is the logic behind a deduction, not its correct name.

Ronk wrote:Even when used in a loop, I think it's still a Type 3 Unique Rectangle to most of us.

I don't see a bivalue cell with candidates "3,6" in row 1 in order for it to be a Type-3 Unique Rectangle. Do you Ronk? Well, in spite of the apparent fact that it looks an UR for most of "you", it is still an AUR for me. Good try Ronk, but you didn't convince me, sorry.

If a naked pair doesn't cause an exclusion in its unit (row, col, or box), but does cause an exclusion as part of an xy-chain, should we then call it an Almost Naked Pair?

Carcul wrote:Also, I think what is really important is the logic behind a deduction, not its correct name.

lb2064 wrote:Pretty neat exercise rep'nA. Creating the deadly pattern to eliminate a candidate is a new technique for me. Thanks for the initial explanation.LB

LB,

Your welcome. If you want to see more examples, check out Carcul's use of Almost Unique Rectangles (which he cited above). Though Carcul often uses them in a slightly different fashion, many of his deductions can be translated into the form:

Set rXcY = a, then... and we get a deadly pattern. This is how I use AUR's for the most part. Also, I recommend checking out the thread on unique rectangles and x-wings. For me, the moral of the story is that there are many overlooked ways of forcing deadly patterns.